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Encyclopedia > Abraham Robinson
Abraham Robinson

Abraham Robinson (October 6, 1918April 11, 1974) was a mathematician who is most widely known for development of non-standard analysis, a mathematically rigorous system whereby infinitesimal and infinite numbers were incorporated into mathematics. Image File history File links Abraham_robinson. ... Image File history File links Abraham_robinson. ... October 6 is the 279th day of the year (280th in leap years). ... 1918 (MCMXVIII) was a common year starting on Tuesday of the Gregorian calendar (see link for calendar) or a common year starting on Wednesday of the Julian calendar. ... April 11 is the 101st day of the year in the Gregorian calendar (102nd in leap years). ... 1974 (MCMLXXIV) was a common year starting on Tuesday. ... Leonhard Euler is considered by many to be one of the greatest mathematicians of all time A mathematician is the person whose primary area of study and research is the field of mathematics. ... Non-standard analysis is that branch of mathematics that formulates analysis using a rigorous notion of infinitesimal, where an element of an ordered field F is infinitesimal if and only if its absolute value is smaller than any element of F of the form 1/n, for n a natural...


He was born to a Jewish family with strong Zionist beliefs, in Waldenburg, Germany, which is now Walbrzych, in Poland. Robinson was in France when the Nazis invaded, and escaped by train and on foot, being alternately questioned by French soldiers suspicious of his German passport and asked by them to share his map, which was more detailed than theirs. He joined the Free French air force, and contributed to the war effort by teaching himself aerodynamics and becoming an expert on the airfoils used in the wings of fighter planes. The word Jew ( Hebrew: יהודי) is used in a wide number of ways, but generally refers to a follower of the Jewish faith, a child of a Jewish mother, or someone of Jewish descent with a connection to Jewish culture or ethnicity and often a combination... A bilingual poster in Romanian and Hungarian promoting a film about Jewish settlement in Palestine, 1930s. ... Waldenburg is the name of several communes Waldenburg, Saxony, Germany Waldenburg, Baden-Württemberg Waldenburg, Switzerland the former German name for Walbrzych, Poland Waldenburg, Arkansas, USA This is a disambiguation page — a navigational aid which lists other pages that might otherwise share the same title. ... Wałbrzych (pronounce: [vawbʒix], German Waldenburg) is a town in south-western Poland with 139,600 inhabitants (1995). ... The Free French Forces (Forces Françaises Libres in French) were French fighters who decided to go on fighting against Germany after the Fall of France and German occupation and to fight against Vichy France in World War II. General Charles de Gaulle was a member of the French Cabinet... This article does not cite its references or sources. ...


After the war, Robinson worked in London, Toronto, and Jerusalem, but ended up at UCLA in 1962. He was becoming well known for his approach of using the methods of mathematical logic to attack problems in analysis and abstract algebra. In particular he "introduced many of the fundamental notions of model theory"[1]. Using these methods, he found a way of using formal logic to show that there are self-consistent nonstandard models of the real number system, which include infinite and infinitesimal numbers. Others, such as Wim Luxemburg, showed that the same results could be achieved using ultrafilters, which made Robinson's work more accessible to mathematicians who lacked training in formal logic. Robinson's book Non-standard Analysis was published in 1965. Robinson was strongly interested in the history and philosophy of mathematics, and often remarked that he wanted to get inside the head of Leibniz, the first mathematician to attempt to articulate clearly the concept of infinitesimal numbers. This article is about the capital of England and the United Kingdom. ... For other uses, see Jerusalem (disambiguation). ... Binomial name Ucla xenogrammus Holleman, 1993 The largemouth triplefin, Ucla xenogrammus, is a fish of the family Tripterygiidae and only member of the genus Ucla, found in the Pacific Ocean from Viet Nam, the Philippines, Palau and the Caroline Islands to Papua New Guinea, Australia (including Christmas Island), and the... Mathematical logic is a subfield of mathematics that is concerned with formal systems in relation to the way that they encode intuitive concepts of mathematical objects such as sets and numbers, proofs, and computation. ... Analysis is the branch of mathematics most explicitly concerned with the notion of a limit, either the limit of a sequence or the limit of a function. ... Abstract algebra is the field of mathematics that studies algebraic structures, such as groups, rings, fields, modules, vector spaces, and algebras. ... In mathematics, model theory is the study of the representation of mathematical concepts in terms of set theory, or the study of the structures that underlie mathematical systems. ... In mathematics, especially in order theory, an ultrafilter is a subset of a partially ordered set (a poset) which is maximal among all proper filters. ... It has been suggested that this article be split into multiple articles. ...


Robinson was at UCLA during the height of the Free Speech Movement and the movement against the Vietnam War. Although he was basically in sympathy with both, he didn't feel at home in the University of California. His colleagues remember him as working hard to accommodate PhD students of all levels of ability by finding them projects of the appropriate difficulty, but he was also unsatisfied with the quality of the graduate students at UCLA. He was courted by Yale, and after some initial reluctance, he moved there in 1967. He died of pancreatic cancer in 1974. The Free Speech Movement was a student protest which began in 1964 - 1965 on the campus of the University of California, Berkeley under the informal leadership of student Mario Savio and others. ... Combatants Republic of Vietnam United States Republic of Korea Thailand Australia New Zealand The Philippines National Front for the Liberation of South Vietnam Democratic Republic of Vietnam People’s Republic of China Democratic Peoples Republic of Korea Strength US 1,000,000 South Korea 300,000 Australia 48,000... “Yale” redirects here. ... Pancreatic cancer (also called cancer of the pancreas) is a malignant tumour within the pancreatic gland. ...


References

  • J. W. Dauben, Abraham Robinson: The Creation of Nonstandard Analysis, A Personal and Mathematical Odyssey, Princeton, NJ: Princeton University Press, 1998
  1. ^ Hodges, W: "A Shorter Model Theory", page 182. CUP, 1997

External links


  Results from FactBites:
 
Non-standard analysis - Wikipedia, the free encyclopedia (2218 words)
Non-standard analysis was introduced in the early 1960s by the mathematician Abraham Robinson.
As developed by him in his papers, it is based on studying models (in particular saturated models) of a theory.
One of these results is the theorem proven by Abraham Robinson and Allen Bernstein that every polynomially compact linear operator on a Hilbert space has an invariant subspace.
  More results at FactBites »

 
 

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